Cochran-Mantel-Haenszel Test

Kategorik · Stratifiye

Cochran-Mantel-Haenszel Test is one of the statistical analyses applied automatically in MerQur. This page illustrates — on a Education Sciences sample dataset — how the analysis is run, what the MerQur output looks like, and how the result is reported in APA 7 format.

🎯 What is it for?

The Cochran-Mantel-Haenszel Test automatically performs all required assumption checks (normality, homogeneity of variance, etc.) for the relevant data type in the background and presents the results with a clear table + chart. Automatic interpretation in the APA 7 standard, effect sizes such as Cohen’s d/η²/R², and 95% confidence intervals are reported.

📌 When is it used?

Statistical analysis of measurements in the Education Sciences domain
To produce APA 7-compatible result tables for academic publications
Hypothesis testing and decision-making processes
Undergraduate / master’s / PhD theses after the appropriate method has been selected

📐 Assumptions

Appropriate scale — Variables must be at the measurement level required by the analysis (nominal/ordinal/interval/ratio)
Independent observations — Observations must come from individuals independent of one another
Sufficient sample size — The minimum n requirement for the analysis must be met
Outlier check — Outliers must be detected and evaluated

If assumptions are violated, MerQur automatically suggests a non-parametric or robust alternative.

🛠 How to do it in MerQur

Load the data. Select the sample file from File → Open. MerQur auto-detects column types.

Select the analysis. From the left side select Cochran-Mantel-Haenszel Test.

Panel assignments (form fields in the program):

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Optional settings. Effect size ✓ · 95% confidence interval ✓ · Assumption checks (automatic).

▶ Run — click the button. Results are produced automatically as a table + chart.

📄 Export to Word. APA 7-formatted report with italic statistical symbols.

📊 Sample Dataset — Education Sciences

ℹ Note: The scenario, MerQur output and interpretation below were produced by actually running the real example dataset in MerQur. Numeric results on your own data will differ; the goal is to show how the analysis is set up and interpreted end-to-end.

🎬 Example File

This analysis is demonstrated on the following example dataset for Education Sciences:

Egitim_Bilimleri/26_cmh_intervention_school.xlsx

🎬 Scenario

Suppose we evaluated an intervention across three different schools and want to know whether it improves student success while accounting for which school students attend. We have 360 students from school A, B, and C, each assigned to either the control or intervention group, with success recorded as yes or no. The research question is whether the intervention is associated with success after controlling for school. The Cochran-Mantel- Haenszel test is appropriate because it tests the group-outcome association across the strata defined by school.

⚙️ Variable Selection

Row variable: group (control/intervention)
Column variable: successful (no/yes)
Stratum variable: school (school-A/school-B/school-C)

Data Preview (First 5 Rows)

student_id	school	group	successful
1	school-A	control	no
2	school-A	control	yes
3	school-A	control	yes
4	school-A	control	yes
5	school-A	control	yes

n = 360 · Columns: student_id, school, group, successful

📈 MerQur Output

COCHRAN-MANTEL-HAENSZEL TEST RESULT ───────────────────────────────────────────── CMH chi-square(1) = 13.89 p < .001 *** Common OR (MH) = 2.36 (95% CI: 1.49 – 3.72) Breslow-Day chi-square(2) = 3.49, p = 0.17 (homogeneous OR) H0 REJECTED

💬 Interpretation

We examined the association between intervention group and achievement while controlling for school (strata) with the CMH test. Even holding school constant the association is significant: common odds ratio 2.36 (p < .001) — stripped of the school confounder, the intervention group’s odds of success are 2.4 times the control’s. The Breslow-Day test is non-significant (p = 0.17), meaning the effect is consistent across all schools (homogeneous OR). CMH is the classic way — very valuable in multi-centre education studies — to control for a third variable (school, class) by stratification.

⚠ Common Mistakes

Misidentifying the data type (e.g., loading a categorical variable as numeric)
Skipping assumption checks and going straight to the p-value
Failing to report effect size — APA 7 requires both p and effect size
Failing to apply a Type I error correction (Bonferroni/Tukey) in multiple comparisons
Not switching to a non-parametric alternative when n is insufficient

📹 Video Walkthrough

Watch the video below for an end-to-end walkthrough of this analysis on a Education Sciences file.

▶ Cochran-Mantel-Haenszel Test — video walkthrough

This analysis is demonstrated on a sample dataset from Anaesthesiology (the steps are identical across disciplines). The link jumps straight to 8:17. Narration is in Turkish.

▶ Watch this analysis (8:17) 📺 All videos

🔀 The same analysis in other disciplines:
🧪 Natural Sciences & Mathematics · 🏛 Architecture, Planning & Design · ⚙ Engineering · 🏥 Health Sciences · 📊 Social, Humanities & Admin Sciences · 🏃 Sport Sciences · 🌾 Agriculture, Forestry & Aquatic

📚 If You Used This Analysis, Cite MerQur

If you performed this analysis using MerQur in a scientific study, please use the citation below as part of your academic citation obligations (APA 7):

Örücü, Ö. K. (2026). MerQur: Integrated Academic Data Analysis & Reporting Platform [Computer software] (Version 1.0.0). https://doi.org/10.53463/merqur.2026001

For BibTeX, RIS, EndNote and the English citation form: all citation formats →

Sources:

American Psychological Association. (2020). Publication manual of the American Psychological Association (7th ed.).
Field, A. (2018). Discovering statistics using IBM SPSS Statistics (5th ed.). Sage.
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Lawrence Erlbaum.